Explanation on “annuities puzzle”

The traditional theory of annuity demand thought a life-cycle consumer who pursued the maximization of consumption utility should fully annuitize all of their savings. The phenomenon that their theoretic conclusion does not accord with the reality was called “annuities puzzle”. Establishing a savings expected utility model that involves term insurance, annuity and security, we discuss the optimal choice of saving behavior of expected utility maximizers. We demonstrate that people without a bequest motive annuitize all savings if the annuities available are actuarially fair. If the annuities available are loading and there is no long-lived gain, or there is a bequest motive, full annuitization is not optimal. The conclusion then explains the “annuities puzzle”.